%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM926+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:51:05 PM UTC 2026
% Result : Theorem 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 19 unt; 0 def)
% Number of atoms : 53 ( 33 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 40 ( 19 ~; 13 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 37 ( 4 sgn 18 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_22_zless__le,axiom,
! [X16,X17] :
( ord_less(int,X16,X17)
<=> ( X16 != X17
& ord_less_eq(int,X16,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zless__le) ).
fof(fact_86_number__of__is__id,axiom,
! [X18] : number_number_of(int,X18) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_number__of__is__id) ).
fof(fact_85_zmult__commute,axiom,
! [X15,X11] : times_times(int,X15,X11) = times_times(int,X11,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zmult__commute) ).
fof(fact_89_zadd__commute,axiom,
! [X15,X11] : plus_plus(int,X15,X11) = plus_plus(int,X11,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zadd__commute) ).
fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( t = one_one(int)
=> ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( ord_less(int,one_one(int),t)
=> ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_0_tpos,axiom,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
fof(c_0_8,negated_conjecture,
~ ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_9,plain,
! [X16,X17] :
( ord_less(int,X16,X17)
<=> ( X16 != X17
& ord_less_eq(int,X16,X17) ) ),
inference(fof_simplification,[status(thm)],[fact_22_zless__le]) ).
fof(c_0_10,negated_conjecture,
! [X48,X49] : plus_plus(int,power_power(int,X48,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X49,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,plain,
! [X180] : number_number_of(int,X180) = X180,
inference(variable_rename,[status(thm)],[fact_86_number__of__is__id]) ).
fof(c_0_12,plain,
! [X174,X175] : times_times(int,X174,X175) = times_times(int,X175,X174),
inference(variable_rename,[status(thm)],[fact_85_zmult__commute]) ).
fof(c_0_13,plain,
! [X129,X130] : plus_plus(int,X129,X130) = plus_plus(int,X130,X129),
inference(variable_rename,[status(thm)],[fact_89_zadd__commute]) ).
fof(c_0_14,plain,
( plus_plus(int,power_power(int,esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk2_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| t != one_one(int) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])])]) ).
fof(c_0_15,plain,
( plus_plus(int,power_power(int,esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk4_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| ~ ord_less(int,one_one(int),t) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])])]) ).
fof(c_0_16,plain,
! [X205,X206] :
( ( ord_less(int,X205,X206)
| X205 = X206
| ~ ord_less_eq(int,X205,X206) )
& ( ~ ord_less(int,X205,X206)
| X205 != X206 )
& ( ~ ord_less(int,X205,X206)
| ord_less_eq(int,X205,X206) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_17,negated_conjecture,
plus_plus(int,power_power(int,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X2,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
number_number_of(int,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
times_times(int,X1,X2) = times_times(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( t != one_one(int)
| plus_plus(int,power_power(int,esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk2_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( ~ ord_less(int,one_one(int),t)
| plus_plus(int,power_power(int,esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk4_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( ~ ord_less_eq(int,X1,X2)
| ord_less(int,X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
ord_less_eq(int,one_one(int),t),
inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).
cnf(c_0_25,negated_conjecture,
plus_plus(int,power_power(int,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X2,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]) ).
cnf(c_0_26,plain,
( one_one(int) != t
| plus_plus(int,power_power(int,esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk2_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_18]),c_0_19]),c_0_20]) ).
cnf(c_0_27,plain,
( ~ ord_less(int,one_one(int),t)
| plus_plus(int,power_power(int,esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk4_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_18]),c_0_19]),c_0_20]) ).
cnf(c_0_28,plain,
( ord_less(int,one_one(int),t)
| one_one(int) = t ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
one_one(int) != t,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
~ ord_less(int,one_one(int),t),
inference(spm,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_31,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_28,c_0_29]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 03:18:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.51 % Version: 3.5.1
% 0.17/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.51 % Starting sh5l with 300s (1) cores
% 0.17/0.51 % new_bool_3 with pid 1576553 completed with status 0
% 0.17/0.51 % Result found by new_bool_3
% 0.17/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.51 % Search class: FGHSM-FFLM32-DFFFFFNN
% 0.17/0.51 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.51 % SubtermCWHack with pid 1576557 completed with status 0
% 0.17/0.51 % Result found by SubtermCWHack
% 0.17/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.51 % Search class: FGHSM-FFLM32-DFFFFFNN
% 0.17/0.51 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.51 % Preprocessing time : 0.003 s
% 0.17/0.51
% 0.17/0.51 % Proof found!
% 0.17/0.51 % SZS status Theorem
% 0.17/0.51 % SZS output start CNFRefutation
% See solution above
% 0.17/0.51 % Parsed axioms : 142
% 0.17/0.51 % Removed by relevancy pruning/SinE : 48
% 0.17/0.51 % Initial clauses : 126
% 0.17/0.51 % Removed in clause preprocessing : 2
% 0.17/0.51 % Initial clauses in saturation : 124
% 0.17/0.51 % Processed clauses : 553
% 0.17/0.51 % ...of these trivial : 31
% 0.17/0.51 % ...subsumed : 244
% 0.17/0.51 % ...remaining for further processing : 277
% 0.17/0.51 % Other redundant clauses eliminated : 1
% 0.17/0.51 % Clauses deleted for lack of memory : 0
% 0.17/0.51 % Backward-subsumed : 6
% 0.17/0.51 % Backward-rewritten : 9
% 0.17/0.51 % Generated clauses : 2190
% 0.17/0.51 % ...of the previous two non-redundant : 1940
% 0.17/0.51 % ...aggressively subsumed : 0
% 0.17/0.51 % Contextual simplify-reflections : 0
% 0.17/0.51 % Paramodulations : 2177
% 0.17/0.51 % Factorizations : 8
% 0.17/0.51 % NegExts : 0
% 0.17/0.51 % Equation resolutions : 4
% 0.17/0.51 % Disequality decompositions : 0
% 0.17/0.51 % Total rewrite steps : 1099
% 0.17/0.51 % ...of those cached : 892
% 0.17/0.51 % Propositional unsat checks : 0
% 0.17/0.51 % Propositional check models : 0
% 0.17/0.51 % Propositional check unsatisfiable : 0
% 0.17/0.51 % Propositional clauses : 0
% 0.17/0.51 % Propositional clauses after purity: 0
% 0.17/0.51 % Propositional unsat core size : 0
% 0.17/0.51 % Propositional preprocessing time : 0.000
% 0.17/0.51 % Propositional encoding time : 0.000
% 0.17/0.51 % Propositional solver time : 0.000
% 0.17/0.51 % Success case prop preproc time : 0.000
% 0.17/0.51 % Success case prop encoding time : 0.000
% 0.17/0.51 % Success case prop solver time : 0.000
% 0.17/0.51 % Current number of processed clauses : 260
% 0.17/0.51 % Positive orientable unit clauses : 47
% 0.17/0.51 % Positive unorientable unit clauses: 7
% 0.17/0.51 % Negative unit clauses : 26
% 0.17/0.51 % Non-unit-clauses : 180
% 0.17/0.51 % Current number of unprocessed clauses: 1460
% 0.17/0.51 % ...number of literals in the above : 3047
% 0.17/0.51 % Current number of archived formulas : 0
% 0.17/0.51 % Current number of archived clauses : 16
% 0.17/0.51 % Clause-clause subsumption calls (NU) : 5443
% 0.17/0.51 % Rec. Clause-clause subsumption calls : 5387
% 0.17/0.51 % Non-unit clause-clause subsumptions : 171
% 0.17/0.51 % Unit Clause-clause subsumption calls : 129
% 0.17/0.51 % Rewrite failures with RHS unbound : 0
% 0.17/0.51 % BW rewrite match attempts : 553
% 0.17/0.51 % BW rewrite match successes : 13
% 0.17/0.51 % Condensation attempts : 0
% 0.17/0.51 % Condensation successes : 0
% 0.17/0.51 % Termbank termtop insertions : 37721
% 0.17/0.51 % Search garbage collected termcells : 1344
% 0.17/0.51
% 0.17/0.51 % -------------------------------------------------
% 0.17/0.51 % User time : 0.045 s
% 0.17/0.51 % System time : 0.005 s
% 0.17/0.51 % Total time : 0.049 s
% 0.17/0.51 % Maximum resident set size: 4056 pages
% 0.17/0.51
% 0.17/0.51 % -------------------------------------------------
% 0.17/0.51 % User time : 0.048 s
% 0.17/0.51 % System time : 0.011 s
% 0.17/0.51 % Total time : 0.059 s
% 0.17/0.51 % Maximum resident set size: 5120 pages
% 0.17/0.51 % E exiting
%------------------------------------------------------------------------------